{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T01:33:16Z","timestamp":1760059996608,"version":"build-2065373602"},"reference-count":22,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T00:00:00Z","timestamp":1753747200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Deanship of Scientific Research and Libraries in Princess Nourah bint Abdulrahman University","award":["RG-1445-0039"],"award-info":[{"award-number":["RG-1445-0039"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>In this study, we establish new oscillation criteria for solutions of the fourth-order differential equation (a\u03d5uu\u2034)+q(u\u2218h)=0, which is of a functional type with a delay. The oscillation behavior of solutions of fourth-order delay equations has been studied using many techniques, but previous results did not take into account the existence of the function \u03d5 except in second-order studies. The existence of \u03d5 increases the difficulty of obtaining monotonic and asymptotic properties of the solutions and also increases the possibility of applying the results to a larger area of special cases. We present two criteria to ensure the oscillation of the solutions of the studied equation for two different cases of \u03d5. Our approach is based on using the comparison principle with equations of the first or second order to benefit from recent developments in studying the oscillation of these orders. We also provide several examples and compare our results with previous ones to illustrate the novelty and effectiveness.<\/jats:p>","DOI":"10.3390\/axioms14080587","type":"journal-article","created":{"date-parts":[[2025,7,29]],"date-time":"2025-07-29T08:00:41Z","timestamp":1753776041000},"page":"587","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Oscillation Theorems of Fourth-Order Differential Equations with a Variable Argument Using the Comparison Technique"],"prefix":"10.3390","volume":"14","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-3850-1022","authenticated-orcid":false,"given":"Osama","family":"Moaaz","sequence":"first","affiliation":[{"name":"Department of Mathematics, College of Science, Qassim University, P.O. Box 6644, Buraydah 51452, Saudi Arabia"}]},{"given":"Wedad","family":"Albalawi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9449-7489","authenticated-orcid":false,"given":"Refah","family":"Alotaibi","sequence":"additional","affiliation":[{"name":"Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia"}]}],"member":"1968","published-online":{"date-parts":[[2025,7,29]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Gyori, I., and Ladas, G.E. (1992). Oscillation Theory of Delay Differential Equations: With Applications, The Clarenden Press. 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